Crystallographical analysis of shear bands initiation and propagation in pure metals

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Crystallographical analysis of shear bands initiation and propagation in pure metals

Ph. Dubois, C. Rey

To cite this version:

Ph. Dubois, C. Rey. Crystallographical analysis of shear bands initiation and propagation in pure metals. Revue de Physique Appliquée, Société française de physique / EDP, 1988, 23 (4), pp.696-696.

�10.1051/rphysap:01988002304069600�. �jpa-00245844�

696

CRYSTALLOGRAPHICAL ANALYSIS OF SHEAR BANDS INITIATION AND PROPAGATION IN PURE METALS

Ph. DUBOIS and C. REY

LPMTM, Université PARIS-NORD - Av. J.B. Clément 93430 - VILLETANEUSE

Revue

Phys. Appl.

(1988)

^1988,

Our purpose ^{was to} determine conditions of shear bands initiation and propagation in pure copper

single ^or polycrystals sollicited by tensile load and rolling.

Tensile _tests were carried out "in situ" on single crystal oriented for double slip, ^{thanks to a SEM.}

So we were able to determine the crystallographi-

cal nature of shear planes for various tensile axis orientation. Four orientations closed to

|001|, |-1,1,3|, |-1,1,2|

|-1,1,1|

investigated. ^{In all cases shear} banding ^occured

in the necking ^{area after a mean} strain of about 55%. "In situ" observations pointed ^{out that the} localization mode was always caracterized by shearing ^{in a} very thin and planar band which width increased with increasing ^strain.

We had compared ^our experimental ^{results to the} prediction of the theoretical model developped by

Pierce

Ill

(2I,

Hutchinson 131

|4|

crystal plasticity ^{was rate} independent, governed by Schmid’s law, ^{moreover the} crystal ^{was oriented}

in double ship deformation for tensile loading.

For such a double orientation, ^a thin band of intense shearing ^limited by ^two nearly parallel planes grew in the crystal (fig.1). The transfor- mation gradient ^{rate F was} supposed ^{to show an} abrupt change of value in the thin band compared

to the bulk one.

According ^{to different authors, the} discontinuity

must be of the form :

where G and N were the shearing ^{vector and the}

unit normal to the band. Traction rates must be continuous across the shear planes, ^{so one must}

have :

where S was the nominal stress tensor.

The misfit between experimental observations and theoretical predictions ^about crystallographical

orientations of shear planes ^{led us to introduce}

in the model some other parameters ^{in order to} take into account :

- the tensile test direction

- the stress field induce by ^{the neck}

- conditions on the strain field compa- tibility.

Fig.1 Shear-band mode for tensile loa- ding.

By ^these formulation we defined "potential ^shear systems" ^{and are} studying ^some criterions in order to determine the more favorable systems.

In polycrystals ^{case, strained} by rolling, ^fidu-

cial grids ^{were set down on the} longitudinal section, in order to point ^{out the} displacement

induced by shear bands and to analyse the inter- action between shear bands and grain boundaries. A 1 MM2 square grid ^{with 5 vm} mesh size and an

average 0.5 um grid ^{line was obtained} by ^a photo-

resist technique, using the beam of a SEM. Our observations, pointed ^{out that} (Fig.2) :

- macroscopical shear bands were constituted of

microscopical ^ones

- shearing intensity ^was proportional ^{to the}

number of microscopical bands activated inside

macroscopical ^ones

- strain increased by elongation of initial shear bands and nucleation of ^new bands in the

vicinity of initial ones.

Previous works on rolled polycrystals ^have reported that shear bands appeared ^{inside somme} especially ^oriented grains. With intend to carac-

terize the conditions of initiation and propa- gation ^{of such} bands, experiments ^on special

oriented bicrystals have been undertaken.

REFERENCES

1 D. PEIRCE J. Mech. Phys. ^{Solids 31} (1983) ^133.

2 M.A. BIOT "Mechanics of Incremental Deforma-

tions", ^edited by Willey (1965).

3 R. HILL and J.W.. HUTCHINSON J. Mech. Phys.

Solids, ²³ (1975) ^239.

4 D. PEIRCE et al Acta Met. 30 (1982) 1087.

Fig.2 Propagation of shear band in rol- led polycrystals.

- Initial bands,...new ^bands.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:01988002304069600